But Barnham does not really scrutinize the issue at all. For all his discussion of "rigor" and error bars in the collection of estimates, it does not consider the various components of the CO2 estimates except for one, which is apparently where most of the high CO2 release estimate comes: the assumption that uranium will be extracted from rock with a uranium content of 0.005% or less. This is the "yellow coal" scenario - at this concentration, using once-through U-235 burning only (boosted by in situ produced actinide burning) as in current reactors, the uranium ore contains no more energy than does coal.
But this is not a likely source of uranium in the future. Seawater is. It contains 1000 times as much uranium as the "yellow coal" ore, and can be extracted at a much lower energy cost, and a lower dollar cost as well.
We can estimate the energy cost of uranium from seawater by considering how it is collected, by immersing special polymer fabrics in seawater, to which the uranium ions attach. Polymers exist that have shown the ability to collect over 10% of their mass in uranium, and may be substantially reusable. The energy cost (and dollar cost) of manufacturing the polymers, deploying them, and stripping the uranium from them is considerably lower than mining and refining "yellow coal" uranium ore. Estimates of current seawater extraction technology are actually lower than the peak spot price of uranium already seen.
Nuclear power opponents dismiss seawater uranium with the argument that it is speculative, since no one produces uranium from this source yet. There is a good reason for that. We haven't exhausted supplies of richer ore yet, and thus don't need it. The fact that no one yet mines uranium ore with a uranium content of 0.005% either somehow does not trouble them in making their projections (the lowest grade ore currently mined is about ten times more concentrated than that).